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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Reconstructing words using queries on subwords or factors

Résumé

We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k 2 n log 2 (n)) words. Two previous upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.
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Dates et versions

hal-03922190 , version 1 (04-01-2023)
hal-03922190 , version 2 (05-02-2023)

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Gwenaël Richomme, Matthieu Rosenfeld. Reconstructing words using queries on subwords or factors. 2023. ⟨hal-03922190v1⟩
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